Non-smooth

Describing something that lacks smoothness or continuity, characterized by abrupt changes, sharp edges, or a lack of gradual variation. It pertains to mathematical functions, surfaces, or processes that exhibit discontinuities, corners, or other features that prevent them from being infinitely differentiable (in calculus terms). This contrasts with smooth objects, which exhibit gradual changes and can be described using continuous derivatives. The term is applicable in diverse fields including mathematics, computer graphics, and signal processing.

Non-smooth meaning with examples

• The jagged peaks of the mountain range presented a non-smooth landscape to the hikers, making navigation challenging. Their uneven surfaces contrasted the gentle curves of the nearby valleys. This non-smooth terrain demanded extra caution, and they needed suitable climbing gear to avoid injury. Their journey required careful planning and consideration of potential hazards in this type of environment.
• The function in the graph was non-smooth because of the sharp corner at x=0, indicating a change in direction with no continuous derivative. Unlike the curves of a parabola, this function's lack of differentiability limited the range of techniques that could be applied. The discontinuous nature made it non-smooth compared to other typical functions often used in models.
• The attempt to render a complex surface using too few polygons resulted in a non-smooth appearance. Instead of seamless curved surfaces, the object appeared blocky. The visual discontinuities hampered the illusion of realism. Fine detailing was lacking. This outcome emphasized the importance of sufficient polygon counts to display the object.
• A noisy signal, where fluctuations are rapid and unpredictable, is often considered non-smooth. Filtering techniques are sometimes applied to reduce this non-smooth signal. It might contain many sudden jumps that are not suitable for analysis using continuous methods. The noise makes the signal difficult to process as well.